No; on Barrayar they're ethnic groups, but they derive from settlers who originated from four specific countries (and who retained cultural and linguistic markers from those countries.) There's no way if you picked a starship of 40,000 people from those specific countries that you'd end up with a lilywhite population unless you were specifically screening on white supremacist grounds, and even then you'd have difficulties.

Also, how do you define an "ethnic" Briton? There've been black Britons here since Roman times, and we're the product of successive waves of immigration before and since.